This invention relates generally to continuous-time filters and, more particularly, to resonators that are critical components in continuous-time filters. A continuous-time filter operates on continuously varying (analog) signals rather than discrete digital signal samples. Although digital signal processing is widely used in communication systems and other applications, there is still a need for continuous-time filters to perform certain critical functions, such as at the point of analog-to-digital (A/D) conversion. One specific area in which the accurate tuning of active filters is important is the world of continuous-time delta-sigma analog-to-digital converters. This type of A/D converter contains at its core a continuous-time “loop filter.” A loop filter is typically composed of a number of resonators that create transfer function “poles” at specific frequencies. The pole frequency (resonant frequency) and Q (quality) value of each resonator are critical factors in ensuring that that the overall closed loop A/D converter is stable and subject to only low noise in a frequency band of interest.
By way of further background, it is worth noting that although filter circuits are often characterized in terms of their frequency response and their characteristics in the time domain, they are typically analyzed and designed in terms of their characteristics in the “s-domain” or “s-plane,” a plane in which a time-domain signal x(t) can be represented as an s-domain signal, which is a function of s, where s is a complex variable in the well known Laplace transform that relates any time-domain signal to its corresponding s-domain form. One of the advantages of representing a continuous-time filter in the s-domain is that the characteristics of the filter can be depicted in the s-plane as points known as poles and zeros. In such a “pole-zero plot,” as it is known, each pole is a point in the s-plane at which the transfer function of the filter becomes very large, and each zero is a point in the s-plane at which the transfer function of the filter falls to near zero. The frequency response of the filter is represented in the s-plane by the variation of the transfer function along the imaginary axis of the s-plane. Therefore, for a resonator circuit a pole on the imaginary axis of the pole-zero plot corresponds to a resonant frequency in the frequency response of the circuit.
The design of continuous-time filters is complicated by the fact that integrated circuit process variations and other factors can skew the filter's most important figures of merit (e.g. the center frequency, bandwidth, and Q factor) such that the constructed end product does not meet the design specification. For example, the accuracy of an integrated filter designed using active-resistor-capacitor (active-RC) techniques depends greatly on the accuracy of the resistors and capacitors available. These components commonly vary by as much as 10-20% from their nominal values in an integrated circuit (IC) environment. There is a need, therefore, for a tuning technique that can compensate for these inaccuracies so that the finished filter can meet the design criteria. The present invention is directed to this end.